A major bottleneck in state-of-the-art algorithms for global dynamic optimization using complete methods is computing enclosures for the solutions of nonlinear parametric differential equations. This paper presents a new algorithm for computing such enclosures, which features a combination of Taylor model propagation and ellipsoidal calculus. The former enables high-order convergence to the exact reachable set as the parameter set shrinks, while the latter mitigates bound explosion compared to interval analysis. The convergence properties of the proposed bounding technique are analyzed and conditions under which higher order convergence can be achieved are given. Implementation details are also discussed and the approach is demonstrated on a numerical case study.
As nanotechnology has developed over the last two decades, some nanostructures, such as nanotubes, nanowires, and nanoparticles, have become very popular. However, recent research has led to the discovery of other, less-common nanoforms, which often serve as building blocks for more complex structures. In an effort to organize the field, the Handbook of Less-Common Nanostructures presents an informal classification based mainly on the less-common nanostructures. A small nanotechnological encyclopedia, this book: Describes a range of little-known nanostructures Offers a unifying vision of the synthesis of nanostructures and the generalization of rare nanoforms Includes a CD-ROM with color versions of more than 100 nanostructures Explores the fabrication of rare nanostructures, including modern physical, chemical, and biological synthesis techniques The Handbook of Less-Common Nanostructures discusses a classification system not directly related to the dimensionality and chemical composition of nanostructure-forming compounds or composite. Instead, it is based mainly on the less-common nanostructures. Possessing unusual shapes and high surface areas, these structures are potentially very useful for catalytic, medical, electronic, and many other applications.
This book provides a detailed description of metal-complex functionalized carbon allotrope forms, including classic (such as graphite), rare (such as M- or T-carbon), and nanoforms (such as carbon nanotubes, nanodiamonds, etc.). Filling a void in the nanotechnology literature, the book presents chapters generalizing the synthesis, structure, properties, and applications of all known carbon allotropes. Metal-complex composites of carbons are described, along with several examples of their preparation and characterization, soluble metal-complex carbon composites, cost-benefit data, metal complexes as precursors of carbon allotropes, and applications. A lab manual on the synthesis and characterization of carbon allotropes and their metal-complex composites is included. Provides a complete description of all carbon allotropes, both classic and rare, as well as carbon nanostructures and their metal-complex composites; Contains a laboratory manual of experiments on the synthesis and characterization of metal-complex carbon composites; Discusses applications in diverse fields, such as catalysis on supporting materials, water treatment, sensors, drug delivery, and devices.
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